Localization in Wireless Sensor Networks - Part 2 ... · Localization in Wireless Sensor Networks...

Localization in Wireless Sensor NetworksPart 2: Localization techniques

Lukasz Mazurek

Department of InformaticsUniversity of Oslo

Cyber Physical Systems, 11.10.2011

Measurement techniques used in localizationOne-hop localization algorithms

Multi-hop localization algorithms

Localization problem in WSN

In a localization problem in WSN we have two groups ofsensors:

Anchors — nodes of the network with known positions.Non-anchors — nodes of the network to be localized.

There are many algotihms leading to localize the non-anchors.

These algorithms use different physical measurements toinvestigate the position of a non-anchor.

Lukasz Mazurek Localization in WSN



Table of Contents

1 Measurement techniques used in localizationAngle-of-arrival (AOA) measurementsDistance-related measurementsReceived signal strength (RSS) profiling measurements

2 One-hop localization algorithmsAOA-based localization techniquesDistance-based localization techniquesRSS-profiling-based localization

3 Multi-hop localization algorithmsConnectivity-based multi-hop localization algorithmsDistance-based multi-hop localization algorithmsCentralized vs distributed algorithms




AOA measurementsDistance-related measurementsRSS profiling measurements

Table of Contents








Angle-of-arrival measurement

In this method we measurethe angle between thetransmitter–receiver line andthe reference direction.

In order to do this we mustuse an anisotropic antenna.

Actually AOA measurementsuse either amplitude orphase response of theantenna.





AOA measurement using antenna’s amplitude response

The rotated beam of the receiveranisotropic antenna

The direction corresponding to themaximum signal strength is takenas the direction of the transmitter

Problem: varying signal strength

Second non-rotating isotropicantenna to normalize the signalstrength.

Use a minimum of two (typically atleast four) stationary antennas withknown, anisotropic antennapatterns.





AOA measurement using antenna’s phase response

Large receiver antenna (relativeto λ) or antenna array.

Phase difference betweenadjacent antenna elements:

2πd cos θ

λ

Problems in case of:

Weak (relative to noise) signals

Strong co-channel interference

Multipath signals





Limitations of AOA measurements

Directivity of the antenna — measurement strongly dependsof antenna angular resolution.

Shadowing — transmitters and receivers must lie inline-of-sight.

Multipath reflections





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Distance-related measurement techniques

Propagation time measurement techniques

Time-difference-of-arrival (TDOA) measurement techniques

Lighthouse approach to distance measurement

Distance estimation using received signal strength (RSS)measurement





Propagation time measurements

One-way propagation time measurements

Measure the difference between the sending time of a signalat the transmitter and the receiving time of the signal at thereceiver.

Requires synchronized local times at the transmitter andreceiver.

Interesting approach: two signals (RF and ultrasonic) sentsimultaneously. Since vsound � c, the time difference betweenthe receipt of signals can be used to calculate the distance.





Propagation time measurements

Roundtrip propagation time measurements

Measure the difference between the time when a signal is sentby a sensor and the time when the returned signal is received.

No synchronization problem.

The major error source: the dalay required for handling thesignal in the second sensor.

A priori known internal delay.Delay measured by the second sensor and sent to the firstsensor to be substracted.





Time-difference-of-arrival measurements

In this method we measure thetime-difference-of-arrival foreach pair of receivers.

TDOA between receiver i andreceiver j is given by:

∆ti ,j = ti − tj ,

where ti , tj — the time when asignal is received at receivers iand j respectively





Time-difference-of-arrival measurements

The accuracy of TDOA measurements will improve when theseparation between receivers increases.

Closely spaced multiple receivers may give rise to multiplereceived signals that cannot be separated.

Overlapping signals due to multipath often cannot be resolved.





Lighthouse approach to distance measurements

Parallel rotating opticalbeam

By measuring the timeduration t that the receiverdwells in the beam we cancalculate the distance fromthe rotational axis of theoptical beam.

d ≈ b

2 sin(ωt/2).





Lighthouse approach to distance measurements

The unknown angular velocity ω can be derived from the timeinterval between the two consecutive detections of the beam.

Adventage: The optical receiver can be of a very small size.

However the transmitter may be large.

This approach requires a direct line-of-sight between theoptical receiver and the transmitter.





Distance estimation using RSS measurements

These techniques are based on a received signal strengthindicator (RSSI).

Advantage: They require no additional hardware.

They are unlikely to significantly impact local powerconsumption, sensor size and cost.

In free space the received power of signal varies as the inversesquare of the distance d between the transmitter and thereceiver

P(d) ∼ 1

d2

In fact the propagation of a signal is affected by reflection,diffraction and scattering.





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RSS profiling measurements

In addition to anchor nodes, a large number of sample pointsare distributed throughout the coverage area of the sensornetwork.

At each sample point, a vector of RSS from all the anchors isobtained.

The collection of all these vectors provides (by extrapolation)a map of the whole region, stored in a central location.

By referring to this map, a non-anchor node can estimate itslocation.




AOA-based localization techniquesDistance-based localization techniquesRSS-profiling-based localization

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One-hop and multi-hop localization techniques

One-hop localization technique

The non-anchor node to be localized is the one-hop neighborof a sufficient number of anchors with known positions.





AOA-based localization techniques

Measured angles βi

Known functions θi (x)

Maximum likelihoodestimator method tofind xt .

In the simpliest caseit’s equivalent to leastsquares method:

xt = arg minn∑

i=1

ε2i

= arg minn∑

i=1

(θi (x)− βi )2





AOA maximum likelihood estimator (MLE)

xt minimizes the following sum:

xt = arg minn∑

i=1

(θi (x)− βi )2

In general, εi = (θi (x)− βi ) are assumed to be zero-meanGaussian noises with variance σ2

i . Therefore in matrix notation:

xt = arg min(θ(x)− β)TS−1(θ(x)− β),

where: θ(x) = (θ1(x), . . . , θn(x)), β = (β1, . . . , βn), and acovariance matrix of εi , S = diag{σ2

1, . . . , σ2n}.





AOA maximum likelihood estimator (MLE)

Minimization problem:


First solution: Newton-Gauss iteration method.

xt,k+1 = xt,k+(θx(xt,k)TS−1θx(xt,k)

)−1θx(xt,k)TS−1 (β − θ(xt,k)) ,

where θx(xt,k) denotes the partial derterivative of θ withrespect to x evaluated at point xt,k .

This method requires an initial estimate close enough to thetrue minimum of the cost function.





AOA — Stansfield approach


Second solution: Stansfield approach. Assumption:measurement error is small enough such that εi ≈ sin εi .

The cost function to minimize becomes:n∑

i=1

sin2(θi (x)− βi )σ2i

We can use the relation

sin(θi (x)− βi ) = sin θi (x) cosβi − cos θi (x) sinβi

=(y − yi ) cosβi − (x − xi ) sinβi

ri,

where ri =√

(x − xi )2 + (y − yi )2.






Cost function to minimize:n∑

i=1

sin2(θi (x)− βi )σ2i

=n∑

i=1

[(y − yi ) cosβi − (x − xi ) sinβi ]2

σ2i r

2i

= (Ax− b)TR−1S−1(Ax− b),

where

A =

sinβ1 − cosβ1...

...sinβn − cosβn

b =

x1 sinβ1 − y1 cosβ1...

xn sinβn − yn cosβn

R = diag{r2

1 , . . . , r2n}






Cost function to minimize:

xt = arg min(Ax− b)TR−1S−1(Ax− b),

Stansfield assumes that the cost function weakly depends onR.

Under these assumptions, the minimization of cost functionwith respect to xt is a well known problem and the solution isgiven by:

xt =(ATR−1S−1A

)−1ATR−1S−1b





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Distance-based localization techniquesGlobal Positioning System (GPS)

31 GPS satellites sending theinformation about satellitespositions and precise time themessage was transmitted.

One-way propagation timemeasurement.

Theoretically, measure of distancefrom 3 satellites is sufficient tocalculate the position of thereceiver.

Practically, the distance fromfourth satellite is necessary forclock synchronization.





Distance-based localization techniques

Generally in a WSN, we measure vector of distancesd̃ = (d̃1, . . . , d̃n) to n anchors.

Let d(x) = (d1(x), . . . , dn(x)) be the vector of real distancesfrom point x to anchors.

Then the location estimation problem can be formulated usinga maximum likelihood approach as:

xt = arg min[d(x)− d̃

]TS−1

[d(x)− d̃

],

where S is the covariance matrix of the distance measurementerrors.

This equation can be solved in similar way to AOA-basedtechnique.





TDOA-based localization techniques

Given the TDOA measurement ∆ti ,jwe get a hyperbola equation

∆ti ,j = ti − tj

=1

c(‖ri − rt‖ − ‖rj − rt‖) ,

for rt . In fact we must consider thedifference between the measuredvalue ∆t̃i ,j and the real value ∆ti ,j .

∆t̃i ,j = ∆ti ,j + εi ,j






For n receivers we get a system of n − 1 linearly independentequations: ∆t̃1,n

...∆t̃n−1,n

=

‖r1−rt‖−‖rn−rt‖

c...

‖rn−1−rt‖−‖rn−rt‖c

+

ε1,n...

εn−1,n

Let ∆t̃ = (∆t̃1,n, . . . ,∆t̃n−1,n), f(r) denotes the vector(

1

c(‖r1 − r‖ − ‖rn − r‖) , . . . , 1

c(‖rn−1 − r‖ − ‖rn − r‖)

)and ε = (ε1,n, . . . , εn−1,n)






We can write our system of equations in the following way:

∆t̃− f(rt) = ε

We want to minimize the sum∑n

i=1 ε2i .

We can again assume that εi is a zero-mean Gaussian noise withvariance σ2

i . Denote the covariance matrix diag{σ21, . . . , σ

2n} by S.

We get the same equation as in AOA case:

rt = arg min[∆t̃− f(r)

]TS−1

[∆t̃− f(r)

]T.

Therefore the recursive solution is

rt,k+1 = rt,k +(fr(rt,k)TS−1fr(rt,k)

)−1fr(rt,k)TS−1

[∆t̃− f(rt,k)

] Lukasz Mazurek Localization in WSN




Lighthouse approach to one-hop localization

Using lighthouse approach wemeasure the distances dX , dY , dZfrom 3 perpendicular axes X ,Y ,Z .

Equations for receiver coordinates:

d2X = y2 + z2

d2Y = z2 + x2

d2Z = x2 + y2

8 solutions corresponding 8quadrants in the coordinate system.

We know a priori in whichquadrant the receiver is located.





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RSS-profiling-based localization

This technique consists of two phases:

Building the RSS map of the entire area,Fitting the measured RSS vector from a non-anchor node intothe appropriate part of the map.

The accuracy of this techique depends on both phasesaccuracy.

The major practical obstacle: changes in the environmentrequire (possibly costly) recalculation of the model.





LANDMARCIndoor Location Sensing Using Active RFID

LANDMARC

An experiment presenting the application of RSS-based localizationtechnique with use of the RFID system.

Radio-frequency identification (RFID)

RFID system consists of RFID readers and RFID tags.

RFID reader can read data emitted from RFID tags.

RFID readers and tags use a defined radio frequency andprotocol to transmit and receive data.

RFID reader used in this experiment has 8 different powerlevels, therefore it can estimate the distance to the RFID tagusing RSS technique.





LANDMARC

16 reference RFID tags withknown positions,

8 tracking RFID tags tolocalize,

4 RFID readers estimating thedistance to tags due tomeasurements on power levels1–8.





LANDMARC

RSS varies due to both static obstructions and dynamichuman movement.

Therefore, direct estimation of the distance to a tracking tagfrom RSS leads to big errors.

Instead we can compare RSS from a tracking tag to RSS froma reference tag with a known position.

Let Pi (t) denotes a RSS from tag t (either tracking orreferenced) measured by reader i (i ∈ {1, . . . , n}).

The distance between tags a and b can be defined as follows:

Ea,b =

√√√√ n∑i=1

(Pi (a)− Pi (b))2





LANDMARC

Coordinates of the tracking tag can be estimated as aweighted mean of coordinates of the k closest (due to Ea,b)reference tags:

rt =k∑

i=1

wi ri .

Empirically, in LANDMARC, weights wi are given by:

wi =1/E 2

t,i∑kj=1 1/E 2

t,j

.

Experiments for different values of k ∈ {1, 2, 3, 4, 5} showedthat the best accuracy of this estimation we get for k = 4.

This result was easy to predict, because all the reference tagswere placed in a grid array.





Summary of LANDMARC experiment

We can implement relatively cheap indoor localization systemwith accuracy under 2 m using RFID.

Unfortunately, RFID products do not provide RSSmeasurement, only report ”detectable” or ”not detectable” ineach of 8 power levels.

Moreover, it takes about 1 minute to scan in all 8 power levels.

Another problem: the power levels detected from two tagsmay be different due to the variation of the chips and circuits,as well as batteries.

Dynamic environment is one of the main reasons forincreasing measurement errors. (A person standing in front ofa tag may greatly increase the error).




Connectivity-based multi-hop localization algorithmsDistance-based multi-hop localization algorithmsCentralized vs distributed algorithms

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Multi-hop localization techniques

Multi-hop localization technique

The non-anchor nodes are not necessarily the one-hop neighbors ofthe anchors.





Connectivity-based multi-hop localization algorithms

Connectivity-based algorithms

They do not rely on any of the described measurementtechniques.

Instead they use the connectivity information who is withinthe communications range of whom.

Connectivity metric

The ratio of the number of transmitter signals succesfullyreceived to the total number of signals from that transmitter.

Transmitters whose connectivity metric exceeds a certainthreshold (e.g. 90%) are called reference points.

A receiver at an unknown location uses the centroid of itsreference points as its location estimate.





Distance vector (DV-hop) approach

All anchors flood their locations to other nodes in the network.

The messages are propagated hop-by-hop and there is ahop-count in the message.

Each node maintains the least number of hops that is awayfrom an anchor.

When an anchor receives a message from another anchor, itestimates the average distance of one hop to this anchor andsends it back to the network as a correction factor.

When receiving the correction factor, a non-anchor node isable to estimate its distance to anchors and performs estimateits location.





Connectivity-based multi-hop localization algorithms

The most attractive feature

Simplicity of algorithms

Limitations

They can only provide a coarse grained estimate of location.

The localization error is highly dependent on the node density,the number of anchors and the network topology (i.e. requiresa high node density, a lot of anchors and a regular network).





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Distance-based multi-hop localization algorithms

The core of distance-based localization algorithms

Use of inter-sensor distance measurements in a sensor network tolocate the entire network.

Centralized algorithms

use a single central processor tocollect all the individualinter-sensor distance data andproduce a map of the entiresensor network.

Distributed algorithms

rely on self-localization of eachnode in the sensor network usingthe distances the node measuresand the local information itcollects from its neighbors.





Centralized distance-based localization algorithms

Centralized distance-based multi-hop localization algorithms

Technique widely used in road traffic monitoring and control,environmental monitoring, health monitoring and precisionagriculture monitoring networks.

Feasible to implement.

High likelihood of providing more accurate location estimatesthan those provided by distributed algorithms.





Centralized distance-based localization algorithms

Multidimensional scaling (MDS) approach

The whole sensor network is divided into smaller groups whereadjacent groups may share common sensors.

Each group contains at least three anchors or sensors whoselocations have already been estimated.

MDS is used to estimate the relative locations of sensors ineach group and build local maps. Local maps are thenstitched together to form an estimated global map by utilizingcommon sensors between adjacent local maps.





Distributed distance-based localization algorithms

Distributed distance-based multi-hop localization algorithms

Extension of the distributed connectivity-based localizationalgorithms.

DV-distance algorithm

Obtained from DV-hop connectivity-based algorithm

Propagates measured distance among neighboring nodesinstead of hop count.





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Centralized vs distributed algorithms

Pro centralized algorithms

Centralized algorithms are likely to provide more accuratelocation estimates than distributed algorithms.

In distributed algorithms error propagation may cause biggerinaccuracies of the final results.

Distributed algorithms are more difficult to design (locallyoptimal algorithms may not perform well in a global sense).

Distributed algorithms generally require multiple iterations toarrive a stable solution and therefore may be slower thancentralized.





Centralized vs distributed algorithms

Pro distributed algorithms

Decentralized localization is harder than centralized — anyalgorithm for decentralized localization can be applied tocentralized problems, but not the reverse.

Centralized algorithms are not feasible to be implemented forlarge scale sensor networks.

Centralized algorithms require higher computationalcomplexity than distributed algoritms.

In large networks distributed algorithms are moreenergy-efficient than centralized algorithms.





Summary

There are many different techniques available for WSNlocalization.

Typically, localization algorithms based on AOA andpropagation time measurements are able to achieve betteraccuracy than RSS techniques.

However, that accuracy is achieved at the expense of higherequipment cost.

It is possible to establish relatively cheap indoor localizationsystem in WSN using RFID equipment.





Bibliography I

Guoqiang Mao, Barıs Fidan and Brian D.O. AndersonWirless Sensor Network Localization Techniques.Computer Networks, 2529-2553, 2007.

Lionel M. Ni and Yunhao Liu.LANDMARC: Indoor Location Sensing using active RFIDWireless Networks 10, 701-710, 2004.


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